TY - JOUR
T1 - A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions
AU - Gil, Juan B.
AU - Tirrell, Jordan O.
N1 - Funding Information:
The authors would like to thank the Department of Mathematics and Statistics and the Hutchcroft fund at Mount Holyoke College for their support.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/6
Y1 - 2020/6
N2 - In this note, we give a simple extension map from partitions of subsets of [n] to partitions of [n+1], which sends δ-distant k-crossings to (δ+1)-distant k-crossings (and similarly for nestings). This map provides a combinatorial proof of the fact that the numbers of enhanced, classical, and 2-distant k-noncrossing partitions are each related to the next via the binomial transform. Our work resolves a recent conjecture of Zhicong Lin and generalizes earlier reduction identities for partitions.
AB - In this note, we give a simple extension map from partitions of subsets of [n] to partitions of [n+1], which sends δ-distant k-crossings to (δ+1)-distant k-crossings (and similarly for nestings). This map provides a combinatorial proof of the fact that the numbers of enhanced, classical, and 2-distant k-noncrossing partitions are each related to the next via the binomial transform. Our work resolves a recent conjecture of Zhicong Lin and generalizes earlier reduction identities for partitions.
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U2 - 10.1016/j.disc.2019.111705
DO - 10.1016/j.disc.2019.111705
M3 - Article
AN - SCOPUS:85075392529
SN - 0012-365X
VL - 343
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 6
M1 - 111705
ER -